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模块:Math
This module provides a number of basic mathematical operations. local yesno = require('Module:Yesno') local getArgs = require('Module:Arguments').getArgs local p = {} -- Holds functions to be returned from #invoke, and functions to make available to other Lua modules. local wrap = {} -- Holds wrapper functions that process arguments from #invoke. These act as intemediary between functions meant for #invoke and functions meant for Lua. -- Helper functions used to avoid redundant code. local function err(msg) -- Generates wikitext error messages. return mw.ustring.format('Formatting error: %s', msg) end local function unpackNumberArgs(args) -- Returns an unpacked list of arguments specified with numerical keys. local ret = {} for k, v in pairs(args) do if type(k) 'number' then table.insert(ret, v) end end return unpack(ret) end local function makeArgArray(...) -- Makes an array of arguments from a list of arguments that might include nils. local args = {...} -- Table of arguments. It might contain nils or non-number values, so we can't use ipairs. local nums = {} -- Stores the numbers of valid numerical arguments. local ret = {} for k, v in pairs(args) do v = p._cleanNumber(v) if v then nums+ 1 = k argsk = v end end table.sort(nums) for i, num in ipairs(nums) do ret+ 1 = argsnum end return ret end local function applyFuncToArgs(func, ...) -- Use a function on all supplied arguments, and return the result. The function must accept two numbers as parameters, -- and must return a number as an output. This number is then supplied as input to the next function call. local vals = makeArgArray(...) local count = #vals -- The number of valid arguments if count 0 then return -- Exit if we have no valid args, otherwise removing the first arg would cause an error. nil, 0 end local ret = table.remove(vals, 1) for _, val in ipairs(vals) do ret = func(ret, val) end return ret, count end -- random }} function wrap.random(args) local first = p._cleanNumber(args1) local second = p._cleanNumber(args2) return p._random(first, second) end function p._random(first, second) math.randomseed(mw.site.stats.edits + mw.site.stats.pages + os.time() + math.floor(os.clock() * 1000000000)) -- math.random will throw an error if given an explicit nil parameter, so we need to use if statements to check the params. if first and second then if first <= second then -- math.random doesn't allow the first number to be greater than the second. return math.random(first, second) end elseif first then return math.random(first) else return math.random() end end -- order | value }} function wrap.order(args) local input_string = (args1 or args.x or '0'); local input_number = p._cleanNumber(input_string); if input_number nil then return err('order of magnitude input appears non-numeric') else return p._order(input_number) end end function p._order(x) if x 0 then return 0 end return math.floor(math.log10(math.abs(x))) end -- precision | value }} function wrap.precision(args) local input_string = (args1 or args.x or '0'); local trap_fraction = args.check_fraction; local input_number; if yesno(trap_fraction, true) then -- Returns true for all input except nil, false, "no", "n", "0" and a few others. See Module:Yesno. local pos = string.find(input_string, '/', 1, true); if pos ~= nil then if string.find(input_string, '/', pos + 1, true) nil then local denominator = string.sub(input_string, pos+1, -1); local denom_value = tonumber(denominator); if denom_value ~= nil then return math.log10(denom_value); end end end end input_number, input_string = p._cleanNumber(input_string); if input_string nil then return err('precision input appears non-numeric') else return p._precision(input_string) end end function p._precision(x) if type(x) 'number' then x = tostring(x) end x = string.upper(x) local decimal = x:find('%.') local exponent_pos = x:find('E') local result = 0; if exponent_pos ~= nil then local exponent = string.sub(x, exponent_pos + 1) x = string.sub(x, 1, exponent_pos - 1) result = result - tonumber(exponent) end if decimal ~= nil then result = result + string.len(x) - decimal return result end local pos = string.len(x); while x:byte(pos) string.byte('0') do pos = pos - 1 result = result - 1 if pos <= 0 then return 0 end end return result end -- max | value1 | value2 | ... }} Note, any values that do not evaluate to numbers are ignored. function wrap.max(args) return p._max(unpackNumberArgs(args)) end function p._max(...) local function maxOfTwo(a, b) if a > b then return a else return b end end local max_value = applyFuncToArgs(maxOfTwo, ...) if max_value then return max_value end end -- min | value1 | value2 | ... }} OR When used with no arguments, it takes its input from the parent frame. Note, any values that do not evaluate to numbers are ignored. function wrap.min(args) return p._min(unpackNumberArgs(args)) end function p._min(...) local function minOfTwo(a, b) if a < b then return a else return b end end local min_value = applyFuncToArgs(minOfTwo, ...) if min_value then return min_value end end -- average | value1 | value2 | ... }} OR Note, any values that do not evaluate to numbers are ignored. function wrap.average(args) return p._average(unpackNumberArgs(args)) end function p._average(...) local function getSum(a, b) return a + b end local sum, count = applyFuncToArgs(getSum, ...) if not sum then return 0 else return sum / count end end -- round | value | precision }} -- function wrap.round(args) local value = p._cleanNumber(args1 or args.value or 0) local precision = p._cleanNumber(args2 or args.precision or 0) if value nil or precision nil then return err('round input appears non-numeric') else return p._round(value, precision) end end function p._round(value, precision) local rescale = math.pow(10, precision or 0); return math.floor(value * rescale + 0.5) / rescale; end -- mod | x | y }} -- function wrap.mod(args) local x = p._cleanNumber(args1) local y = p._cleanNumber(args2) if not x then return err('first argument to mod appears non-numeric') elseif not y then return err('second argument to mod appears non-numeric') else return p._mod(x, y) end end function p._mod(x, y) local ret = x % y if not (0 <= ret and ret < y) then ret = 0 end return ret end -- gcd | value 1 | value 2 | value 3 | ... }} -- function wrap.gcd(args) return p._gcd(unpackNumberArgs(args)) end function p._gcd(...) local function findGcd(a, b) local r = b local oldr = a while r ~= 0 do local quotient = math.floor(oldr / r) oldr, r = r, oldr - quotient * r end if oldr < 0 then oldr = oldr * -1 end return oldr end local result, count = applyFuncToArgs(findGcd, ...) return result end -- precision_format | number | precision }} function wrap.precision_format(args) local value_string = args1 or 0 local precision = args2 or 0 return p._precision_format(value_string, precision) end function p._precision_format(value_string, precision) -- For access to Mediawiki built-in formatter. local lang = mw.getContentLanguage(); local value value, value_string = p._cleanNumber(value_string) precision = p._cleanNumber(precision) -- Check for non-numeric input if value nil or precision nil then return err('invalid input when rounding') end local current_precision = p._precision(value) local order = p._order(value) -- Due to round-off effects it is neccesary to limit the returned precision under -- some circumstances because the terminal digits will be inaccurately reported. if order + precision >= 14 then orig_precision = p._precision(value_string) if order + orig_precision >= 14 then precision = 13 - order; end end -- If rounding off, truncate extra digits if precision < current_precision then value = p._round(value, precision) current_precision = p._precision(value) end local formatted_num = lang:formatNum(math.abs(value)) local sign -- Use proper unary minus sign rather than ASCII default if value < 0 then sign = '−' else sign = '' end -- Handle cases requiring scientific notation if string.find(formatted_num, 'E', 1, true) ~= nil or math.abs(order) >= 9 then value = value * math.pow(10, -order) current_precision = current_precision + order precision = precision + order formatted_num = lang:formatNum(math.abs(value)) else order = 0; end formatted_num = sign .. formatted_num -- Pad with zeros, if needed if current_precision < precision then local padding if current_precision <= 0 then if precision > 0 then local zero_sep = lang:formatNum(1.1) formatted_num = formatted_num .. zero_sep:sub(2,2) padding = precision if padding > 20 then padding = 20 end formatted_num = formatted_num .. string.rep('0', padding) end else padding = precision - current_precision if padding > 20 then padding = 20 end formatted_num = formatted_num .. string.rep('0', padding) end end -- Add exponential notation, if necessary. if order ~= 0 then -- Use proper unary minus sign rather than ASCII default if order < 0 then order = '−' .. lang:formatNum(math.abs(order)) else order = lang:formatNum(order) end formatted_num = formatted_num .. '×10' .. order .. '' end return formatted_num end -- Helper function that interprets the input numerically. If the input does not appear to be a number, attempts evaluating it as a parser functions expression. function p._cleanNumber(number_string) if type(number_string) 'number' then -- We were passed a number, so we don't need to do any processing. return number_string, tostring(number_string) elseif type(number_string) ~= 'string' or not number_string:find('%S') then -- We were passed a non-string or a blank string, so exit. return nil, nil; end -- Attempt basic conversion local number = tonumber(number_string) -- If failed, attempt to evaluate input as an expression if number nil then local frame = mw.getCurrentFrame() local attempt = frame:preprocess(' ') attempt = tonumber(attempt) if attempt ~= nil then number = attempt number_string = tostring(number) else number = nil number_string = nil end else number_string = number_string:match("^%s*(.-)%s*$") -- String is valid but may contain padding, clean it. number_string = number_string:match("^%+(.*)$") or number_string -- Trim any leading + signs. if number_string:find('^%-?0xX') then -- Number is using 0xnnn notation to indicate base 16; use the number that Lua detected instead. number_string = tostring(number) end end return number, number_string end -- Wrapper function that does basic argument processing. This ensures that all functions from #invoke can use either the current frame or the parent frame, and it also trims whitespace for all arguments and removes blank arguments. local function makeWrapper(funcName) return function (frame) local args = getArgs(frame) -- Argument processing is left to Module:Arguments. Whitespace is trimmed and blank arguments are removed. return wrapfuncName(args) end end for funcName in pairs(wrap) do pfuncName = makeWrapper(funcName) end return p